You always wanted to discover which investments or projects are independent
to reduce the risks of systematic failures. However you always knew that once the
data under analysis has been digitized with a finite number of samples there is no way
you could prove the independence.
The traditional solution was based on the usage of Pearson correlation coefficients.
However this is in general an unreliable instrument since it's purpose is to find
how much of the general behavior of one signal can be predicted from a linear
translation of the second signal. Even more advanced correlations fail to give an
answer because there is no fundamental way of responding this question only with
mathematical tools.
To help you with these cases we run an Independent Component Analysis and decide whether
the relation between the data sets implies a substantial influence or just noise. The
decompositions may even help you predict trends hard to see otherwise.
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